, Kirk got the chair in recognition of 2 things:
1) he saved the Earth. That's a biggie.
2) When everyone in the command stuff wanted to do one thing, Kirk followed his gut instinct and said, "No, we need to do this instead", and he was proved to be right. In a commander, that is more valuable than all the spit and polish and by the rules you can name.
It was also pointed out by Bob Orci in the Q&A thread that the time between the destruction of the Narada and the ceremony at Star Fleet where Kirk is commissioned is a little vague, so he could have completed whatever he needed to, with the recommendation of Spock and Pike, to become Captain. That's how I'm reading it, I'm fine with that.